Question

If a perimeter of a room is 78 feet, what is the area of the floor of the room?

Answer 1

The perimeter doesn't tell you the area, and neither of them
can be calculated by knowing the other one.

Check this out:

Dimensions   Perimeter   Area      .

1  by  38              78          38 square feet
2  by  37              78          74 square feet         
3  by  36              78         108 square feet         
5  by  34              78         170 square feet         
10  by  29            78         290 square feet         
15  by  24            78         360 square feet         
17  by  22            78         374 square feet         
19  by  20            78         380 square feet         
19.5 by 19.5        78          380.25 square feet

Nine same perimeters, nine different areas !

Here's one more ... a long skinny one:

1 inch by 38ft 11in     Perimeter = 78 ft.    Area = 3.24 square feet.